Secrecy Capacity Region of a Multi-Antenna Gaussian Broadcast Channel with Confidential Messages

Abstract: In wireless data networks, communication is particularly susceptible to eavesdropping due to its broadcast nature. Security and privacy systems have become critical for wireless providers and enterprise networks. This paper considers the problem of secret communication over the Gaussian broadcast channel, where a multi-antenna transmitter sends independent confidential messages to two users with information-theoretic secrecy. That is, each user would like to obtain its own confidential message in a reliable and safe manner. This communication model is referred to as the multi-antenna Gaussian broadcast channel with confidential messages (MGBC-CM). Under this communication scenario, a secret dirty-paper coding scheme and the corresponding achievable secrecy rate region are first developed based on Gaussian codebooks. Next, a computable Sato-type outer bound on the secrecy capacity region is provided for the MGBC-CM. Furthermore, the Sato-type outer bound prove to be consistent with the boundary of the secret dirty-paper coding achievable rate region, and hence, the secrecy capacity region of the MGBC-CM is established. Finally, two numerical examples demonstrate that both users can achieve positive rates simultaneously under the information-theoretic secrecy requirement.

• The paper develops a novel secret dirty-paper coding (S-DPC) scheme using Gaussian codebooks and double-binning to enable reliable and confidential transmission.
• A computable outer bound matches the S-DPC achievable region, characterizing the secrecy capacity region and showing both users can achieve positive secret rates if channel vectors are linearly independent.
• The findings provide theoretical limits for secure communication in multi-antenna systems and suggest practical strategies like S-DPC for secure data transmission protocols.

An Overview of the Secrecy Capacity Region in Multi-Antenna Gaussian Broadcast Channels with Confidential Messages

This paper addresses a significant challenge in wireless communication: the security of data transmission over broadcast channels. Specifically, it investigates the secrecy capacity region of the multi-antenna Gaussian broadcast channel with confidential messages (MGBC-CM). In such a channel, a transmitter, equipped with multiple antennas, sends independent confidential messages to two users while ensuring information-theoretic secrecy. Each user aims to securely receive its intended message despite the presence of potential eavesdropping by the other user.

Key Contributions

The central contributions of the paper include:

1. Secret Dirty-Paper Coding Scheme: The authors develop a novel secret dirty-paper coding (S-DPC) scheme tailored to the problem of secret communication in the MGBC-CM. This scheme leverages Gaussian codebooks and is notable for enabling both reliable transmission and maintaining confidentiality by utilizing a double-binning technique.
2. Computable Outer Bound: An outer bound on the secrecy capacity region is derived using a computable Sato-type methodology. This bound is shown to be consistent with the achievable rate region provided by the S-DPC, effectively characterizing the secrecy capacity region for the MGBC-CM.
3. Theoretical and Numerical Validation: Through theoretical proofs and numerical examples, the paper demonstrates that both users can achieve positive secrecy rates simultaneously. This is contingent upon the linear independence of the channel attenuation vectors experienced by the two users.

Implications

The implications of this paper are twofold:

• Theoretical Advancement: By establishing the boundary of the secrecy capacity region, this work provides a deeper understanding of information-theoretic limits and the potential of multi-antenna systems in secure communication. It highlights the synergistic role of multiple antennas in enhancing secrecy capabilities, a critical factor when considering eavesdropping in broadcast scenarios.
• Practical Implementation: The derived results suggest practical strategies for secure communication systems, where the deployment of multiple antennas can mitigate the vulnerabilities inherent to wireless channels. The employment of the S-DPC scheme offers pathways to implement secure data transmission protocols in real-world applications, including enterprise networks and sensitive communication environments.

Future Directions

The work opens several avenues for future research, such as:

• Extension to More Users and Antenna Configurations: While this paper focuses on a two-user setup, extending the framework to more complex scenarios with additional users and diverse antenna configurations would be beneficial.
• Hardware and Algorithmic Optimization: Investigating the practical deployment of the S-DPC and the computational requirements inherent to its implementation would enhance the applicability of these theoretical constructs.
• Integration with Modern Wireless Standards: Aligning these results with contemporary and future wireless communication standards, such as 5G and beyond, could facilitate secure data communication at scale.

Overall, this paper significantly advances the understanding of secure communications in multi-antenna Gaussian broadcast channels and sets a foundation for further explorations into pragmatic and theoretical aspects of information-theoretic secrecy in wireless networks.